1.2 KiB
1.2 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f53e1000cf542c510051 | Problem 466: Distinct terms in a multiplication table | 5 | 302141 | problem-466-distinct-terms-in-a-multiplication-table |
--description--
Let P(m,n) be the number of distinct terms in an m×n multiplication table.
For example, a 3×4 multiplication table looks like this:
\begin{array}{c}
× & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} \\\\
\mathbf{1} & 1 & 2 & 3 & 4 \\\\
\mathbf{2} & 2 & 4 & 6 & 8 \\\\
\mathbf{3} & 3 & 6 & 9 & 12
\end{array}$$
There are 8 distinct terms {1, 2, 3, 4, 6, 8, 9, 12}, therefore $P(3, 4) = 8$.
You are given that:
$$\begin{align}
& P(64, 64) = 1\\,263, \\\\
& P(12, 345) = 1\\,998, \text{ and} \\\\
& P(32, {10}^{15}) = 13\\,826\\,382\\,602\\,124\\,302. \\\\
\end{align}$$
Find $P(64, {10}^{16})$.
# --hints--
`multiplicationTable()` should return `258381958195474750`.
```js
assert.strictEqual(multiplicationTable(), 258381958195474750);
```
# --seed--
## --seed-contents--
```js
function multiplicationTable() {
return true;
}
multiplicationTable();
```
# --solutions--
```js
// solution required
```